Answer:
y = - 5(x - 1)² + 5
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (1, 5), hence
y = a(x - 1)² + 5
To find a substitute the coordinates of the root (2, 0) into the equation
0 = a + 5 ⇒ a = - 5
y = - 5(x - 1)² + 5 ← in vertex form
Expand (x - 1)² and rearrange
y = - 5(x² - 2x + 1) + 5
= - 5x² + 10x - 5 + 5
y = - 5x² - 10x ← in standard form
